Background The awareness in reproductive epidemiology of potential structural zeros, defined as impossible combinations of covariate values, has been limited compared to studies of random or sampling zeros. None of the many studies of parity (number of children) and age at first birth (AFB) have analysed or discussed the strong interdependency of high parity and AFB. Here we introduce statistical methods for estimating relative risk (RR) for a breast cancer diagnosis in prospective studies with structural zeros using Cox proportional hazard models. Methods Information on parity and age at marriage for 385.816 women was collected in the 1960 Norwegian Census. Women aged 45–90 years were followed to the end of 2005 based on linkages to the Cancer Registry of Norway identifying 16 905 incident breast cancer diagnoses. The new methodology handles structural zeros in Cox proportional hazard model making it possible to separate the effect of parity and AFB. The model also estimates the effect of increases or decreases in RR for each additional child independently. Results In a full model each additional child was associated with a relative risk (RR) of 0.89 (95% CI; 0.88–0.90) or an 11% reduction per child over the entire fertility range of 1–15 children. The effect of AFB was reduced in the same model and only had impact on the first three children. The effect of early birth was less than one additional child. Conclusion New methods for handling structural zeros in Cox hazards analyses demonstrated a shift in the interpretation towards stronger effect of parity and less of AFB.
Holden et al. (2026) studied this question.